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Article Dans Une Revue Theoretical Computer Science Année : 2003

A solution to the problem of (A,B)-invariance for series

Résumé

The aim of this article is to study a standard problem of control theory, the (A,B)-invariance problem, which amounts to computing a maximal element X subject to conditions of the form AX less-than-or-equals X+B and X less-than-or-equals K. We give a solution to the problem in the framework of formal series over particular complete idempotent semirings. Over finite idempotent semirings, we show that, under the assumption that B and K are recognizable series, the maximal solution exists and is also recognizable. We obtain a similar result for the infinite tropical semiring, with additional hypothesis that the series A is a language, but the notion of recognizable series has to be extended to the weaker notion of pseudo-recognizable series.
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Dates et versions

hal-00019867 , version 1 (28-02-2006)

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  • HAL Id : hal-00019867 , version 1

Citer

Ines Klimann. A solution to the problem of (A,B)-invariance for series. Theoretical Computer Science, 2003, 293/1, pp.115-139. ⟨hal-00019867⟩
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